Button have down arrow right side of it and you can set menu of it from designer:

With ShowMenuUnderCursor:

MenuButton class:
public class MenuButton : Button
{
[DefaultValue(null)]
public ContextMenuStrip Menu { get; set; }
[DefaultValue(false)]
public bool ShowMenuUnderCursor { get; set; }
protected override void OnMouseDown(MouseEventArgs mevent)
{
base.OnMouseDown(mevent);
if (Menu != null && mevent.Button == MouseButtons.Left)
{
Point menuLocation;
if (ShowMenuUnderCursor)
{
menuLocation = mevent.Location;
}
else
{
menuLocation = new Point(0, Height - 1);
}
Menu.Show(this, menuLocation);
}
}
protected override void OnPaint(PaintEventArgs pevent)
{
base.OnPaint(pevent);
if (Menu != null)
{
int arrowX = ClientRectangle.Width - Padding.Right - 14;
int arrowY = (ClientRectangle.Height / 2) - 1;
Color color = Enabled ? ForeColor : SystemColors.ControlDark;
using (Brush brush = new SolidBrush(color))
{
Point[] arrows = new Point[] { new Point(arrowX, arrowY), new Point(arrowX + 7, arrowY), new Point(arrowX + 3, arrowY + 4) };
pevent.Graphics.FillPolygon(brush, arrows);
}
}
}
}